I live in California and visit Yosemite several times a year. I'd say I use the 24-105L & 17-40L the most, followed by my 70-200. You may not go beyond 24mm often, but it's useful at times. For example, the most heavily visited area is the valley, where you'll be at the foot of tall cliffs, probably shooting up, trying to include as much as possible (waterfalls, granite formations etc.). Many locations will force you to be closer, because of trees, cliffs, and other natural barriers; you can't simply back up a bit. There will also be wide vistas you'll probably want to shoot. Of course, you can attempt to merge shots together.
The roads are windy and a bit narrow through the mountains, so I'd highly suggest renting as small an RV as you can, especially if you're not used to driving a large vehicle. Plus you'll be in unfamiliar territory.
From what I've read on TripAdvisor forums, a lot of visitors will visit the Big Sur/Monterey/Carmel area in between San Francisco and Yosemite. It's one of my personal favorite areas to visit, and I'd highly recommend it. Big Sur has stretch of highway along some very beautiful, dramatic coastline, some waterfalls (McWay Falls), beaches, etc. Carmel's 17-Mile drive is beautiful, Monterey has a lot of tourist things to do such as a great aquarium, and Point Lobos preserve is a beautiful spot with lots of amazing hikes.
I'm not sure what roads you'll be taking from Yosemite to Grand Canyon/Vegas, but consider leaving Yosemite by Tioga Road. There's lots of nice things to see on the way. Even if you don't get out and go for long hikes, there are still some great viewing spots right off the road. Also, after you exit Yosemite, you can stop at Mono Lake for a bit before heading south. If you're interested, there's also the old ghost town of Bodie a few miles north.
There's supposed to be some other great stops along there south of Mono Lake but I've never headed that way myself.